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AIP conference proceedings

Monte Carlo simulation of an antiferromagnetic spin-1/2 Ising system on the square lattice

S. Sudhagar, N. Baskaran

Published Jan 1, 2012• 0 citations
Publisher

Abstract

We have studied the thermodynamic and magnetic properties of the spin 1/2 XXZ Ising model on a two dimensional square lattice using Monte Carlo simulation, in the presence of transverse magnetic field for varying lattice sizes (N=8-40) and exchange interaction strengths. The variations in specific heat and susceptibility for different N values is almost negligible, except for N=8. Interestingly, the magnetization showed large variation with N. This could be attributed to the increase in the disorder of spin alignment with increasing N.

DOI
10.1063/1.4709911

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We have studied the thermodynamic and magnetic properties of the spin 1/2 XXZ Ising model on a two dimensional square lattice using Monte Carlo simulation, in the presence of transverse magnetic field for varying lattice sizes (N=8-40) and exchange interaction strengths. The variations in specific heat and susceptibility for different N values is almost negligible, except for N=8. Interestingly, the magnetization showed large variation with N. This could be attributed to the increase in the disorder of spin alignment with increasing N.
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Many problems in statistical physics resist exact solution once the number of interacting particles becomes large, and the two-dimensional Ising model is a classic case where numerical simulation fills that gap. This paper reports a Monte Carlo study of the two-dimensional Ising model using the Metropolis algorithm, undertaken to examine how magnetization, internal energy, specific heat, and magnetic susceptibility change with temperature. Spin configurations were generated on a square lattice under periodic boundary conditions, with each proposed spin flip accepted or rejected according to the Boltzmann weight of the resulting energy change. The simulation reproduces the expected transition from an ordered ferromagnetic state at low temperature to a disordered paramagnetic state at high temperature, with magnetization falling sharply and both specific heat and susceptibility peaking near a critical temperature of Tc ≈ 2.3–2.4 (in units of J/kB), consistent with the exact value obtained analytically for this system. These results confirm that the Metropolis algorithm, despite its simplicity, remains a dependable tool for locating second-order phase transitions and extracting thermodynamic quantities in lattice spin systems, and the same computational framework can be adapted to more elaborate models used in condensed matter and materials research.
Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.
In this work we study a disordered binary Ising model on the square lattice. The model system consists of two different particles with spin-1/2 and spin-1, which are randomly distributed on the lattice. It has been considered only spin nearest-neighbor exchange interactions with J>0J>0J>0. This system can represent a disordered magnetic binary alloy AxB1−xA_{x}B_{1-x}Ax​B1−x​, obtained from the high temperature quenching of a liquid mixture. The results were obtained by the use of Monte Carlo simulations for several lattice sizes LLL, temperature TTT and concentration xxx of ions AAA with spin-1/2. We found its critical temperature, through the reduced fourth-order Binder cumulant for the several values of the concentration xxx of particles (spin-1/2, spin-1), and also the magnetization, the susceptibility and the specific heat as a function of temperature TTT.